Equilibrium configurations of plasma in the approximation of two-fluid magnetohydrodynamics with electron inertia taken into account

A single-fluid version of the equations of two-fluid magnetohydrodynamics is obtained. This paper is concerned with the following topics: derivation of the energy conservation law; proof of degenerate ellipticity of the the generalized Ampère's law; passage to the limit to the equations of the classical magnetohydrodynamics; derivation of plasmastatics equations that generalize the Grad-Shafranov equations and that belong to the class of equations of mixed type: elliptic for dense plasma and hyperbolic for rarefied plasma; analytical and numerical analysis of their solutions for the θ-pinch and z-pinch. © 2009 Springer Science+Business Media, Inc.